Exhibit 5.1

609 Main Street
Houston, TX 77002
United States   +1 713 836 3600   www.kirkland.com   Facsimile:
+ 1 713 836 3601

September 15, 2023

NET Power Inc.
404 Hunt Street, Suite 410
Durham, North Carolina 27701

Ladies and Gentlemen:

We have acted as counsel to NET Power Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-l (File No. 333-273183), initially filed by the Company with the Securities and Exchange Commission (the “Commission”) on July 7, 2023 (such Registration Statement as subsequently amended or supplemented, the “Registration Statement”), relating to the offer and sale from time to time by the selling securityholders named in the prospectus contained in the Registration Statement of (i) up to 204,903,904 shares of the Company’s Class A Common Stock, par value $0.0001 (“Class A Common Stock”), which consist of (a) 54,044,995 shares of Class A Common Stock (the “PIPE Shares”) issued in private placements that closed substantially concurrently with the consummation of the Merger (as defined herein), (b) 2,500 shares of Class A Common Stock (the “Sponsor Shares”) issued to Rice Acquisition Sponsor II LLC (“Sponsor”) in a private placement prior to the consummation of the initial public offering (the “IPO”) of Rice Acquisition Corp. II (“RONI”), (c) 10,900,000 shares of Class A Common Stock issuable upon exercise of the Private Placement Warrants (as defined herein), (d) 7,432,688 shares of Class A Common Stock (the “Sponsor Conversion Shares”) issuable upon redemption of the 7,432,688 units of NET Power Operations LLC (f/k/a Rice Acquisition Holdings II LLC and referred to herein as “Opco”) held by the initial shareholders of RONI or transferees thereof, all of which were issued prior to the consummation of the IPO, (e) 132,205,114 shares of Class A Common Stock (the “Merger Shares”) issued or issuable upon redemption of the 132,205,114 units of Opco issued as consideration upon consummation of the Merger to the Legacy NET Power Holders (as defined herein), and (f) 318,607 shares of Class A Common Stock (the “JDA Shares”) issuable upon the redemption of the 318,607 units of Opco issued to Baker Hughes Energy Services LLC (an affiliate of Baker Hughes Company) for services provided by Nuovo Pignone International, S.r.l. (an affiliate of Baker Hughes Company) pursuant to the Amended and Restated JDA (as defined herein) and (ii) up to 10,900,000 warrants (the “Private Placement Warrants”) issued to Sponsor in a private placement that closed simultaneously with the consummation of the IPO.

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NET Power Inc.

September 15, 2023

Page 2

For purposes of this opinion letter, the following terms have the meanings specified below:

“Amended and Restated JDA” means the Amended and Restated Joint Development Agreement, dated December 13, 2022, by and among Old NET Power, RONI, RONI Opco, Nuovo Pignone International, S.r.l. and Nuovo Pignone Tecnologie S.r.l., as amended, supplemented or otherwise modified from time to time in accordance with its terms.

“Business Combination Agreement” means the Business Combination Agreement, dated as of December 13, 2022, by and among RONI, RONI Opco, Buyer, Merger Sub and Old NET Power, as amended by the First Amendment to the Business Combination Agreement, dated as of April 23, 2023, by and between Buyer and Old NET Power.

“Buyer” means Topo Buyer Co, LLC, a Delaware limited liability company and a direct, wholly owned subsidiary of Opco (following the Domestications) or of RONI Opco (prior to the Domestications).

“Domestications” means (i) the change of RONI’s jurisdiction of registration by deregistering as a Cayman Islands exempted company and continuing and domesticating as a corporation registered under the laws of the State of Delaware, upon which RONI changed its name to “NET Power Inc.” and (ii) the change of RONI Opco’s jurisdiction of registration by deregistering as a Cayman Islands exempted company and continuing and domesticating as a limited liability company registered under the laws of the State of Delaware, upon which RONI Opco changed its name to “NET Power Operations LLC.”

“Legacy NET Power Holders” means the holders of equity securities of Old NET Power prior to the consummation of the Merger.

“Merger” means the merger of Merger Sub with and into Old NET Power pursuant to the Business Combination Agreement, in which Old NET Power survived and became a direct, wholly owned subsidiary of Buyer.

“Merger Sub” means Topo Merger Sub, LLC, a Delaware limited liability company and a direct, wholly owned subsidiary of Buyer.

“Old NET Power” means, prior to the consummation of the Merger, NET Power, LLC, a Delaware limited liability company.

“Opco LLCA” means the Second Amended and Restated Limited Liability Company Agreement of Opco, dated as of June 8, 2023, as it may be amended from time to time.

NET Power Inc.

September 15, 2023

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“Private Placement Warrants Purchase Agreement” means the Private Placement Warrants and Warrant Rights Purchase Agreement, dated as of June 15, 2021, by and among RONI, RONI Opco and Sponsor.

“Private Placement Warrant Shares” means the shares of Class A Common Stock underlying the Private Placement Warrants.

“RONI Opco” means Rice Acquisition Holdings II LLC, a Cayman Islands limited liability company and direct subsidiary of RONI, prior to the Domestications.

“Securities” means the shares of Class A Common Stock and the Private Placement Warrants covered by the Registration Statement.

“Securities Agreements” means the Subscription Agreements, the Private Placement Warrants Purchase Agreement and the Opco LLCA.

“Subscription Agreements” means, collectively, (i) the subscription agreements entered into between RONI and certain investors, pursuant to which such investors agreed to purchase, via private placements that closed substantially concurrently with the consummation of the Merger, an aggregate of 54,044,995 shares of Class A Common Stock, (ii) the Securities Subscription Agreement, dated February 8, 2021, between RONI and Sponsor, and (iii) the Securities Subscription Agreement, dated February 26, 2021, between the Sponsor and RONI Opco.

“Warrant Agreement” means the Warrant Agreement, dated as of June 15, 2021, by and among RONI, RONI Opco and Sponsor.

For purposes of this opinion letter, we have reviewed the Securities Agreements, the Warrant Agreement (including the form of warrant set forth therein), the Business Combination Agreement, the Amended and Restated JDA and the Certificate of Incorporation of the Company (the “Charter”) as well as the Registration Statement. In addition, we have reviewed originals, or duplicates or certified or conformed copies, of corporate records and other instruments as we have deemed necessary for the purpose of this opinion letter, including the corporate and organizational documents of the Company and minutes and records of the corporate proceedings of the Company with respect to the issuance of the Securities, and such certificates or comparable documents of public officials and of officers and representatives of the Company and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth.

NET Power Inc.

September 15, 2023

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In rendering the opinions set forth below, we have assumed the genuineness of the signatures of persons signing all documents in connection with which this opinion is rendered and the authority of such persons signing on behalf of the parties thereto other than the Company or its subsidiaries, the due authorization, execution and delivery of all documents by the parties thereto other than the Company or its subsidiaries, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies, and the authenticity of the originals of such latter documents. We also have assumed that, at the time of the issuance and delivery of any Private Placement Warrant Shares, Sponsor Conversion Shares, Merger Shares or JDA Shares, the applicable Securities Agreements will be the valid and legally binding obligation of each party thereto other than the Company and Opco, as applicable. We have also assumed that, with respect to the issuance of any Private Placement Warrant Shares, the amount of valid consideration paid in respect of such shares will equal or exceed the par value of such shares. As to any facts material to the opinions expressed herein that we have not independently established or verified, we have relied upon statements and representations of officers and other representatives of the Company and others.

In rendering the opinions set forth below, we have assumed further that, at the time of the issuance and delivery of any Private Placement Warrant Shares, Sponsor Conversion Shares, Merger Shares or JDA Shares, (i) the Company will be validly existing and in good standing under the law of the jurisdiction in which it is organized, (ii) the issuance and delivery by the Company of such shares pursuant to the applicable Securities Agreement will not (a) constitute a breach or violation of its organizational documents, (b) violate any applicable law (except that no such assumption is made with respect to the internal law of New York or the Delaware General Corporation Law (the “DGCL”), assuming there shall not have been any change in such laws affecting the validity or enforceability of the applicable Securities Agreements and such shares), (c) constitute a breach or default under any agreement or instrument then binding upon the Company, or (d) violate any restriction imposed by any court or governmental body having jurisdiction over the Company, (iii) the issuance and delivery by the Company of such shares pursuant to the applicable Securities Agreement will comply with all applicable regulatory requirements, and (iv) the authorization of such shares by the Company will not have been modified or rescinded, and there will not have occurred any change in law affecting the validity, legally binding character or enforceability of such shares.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that:

1. The PIPE Shares and the Sponsor Shares are validly issued, fully paid and non-assessable.

2. Assuming the due issuance and delivery of the Private Placement Warrant Shares, upon payment therefor in accordance with the Warrant Agreement and otherwise in accordance with the provisions of such agreement, the Charter, the Private Placement Warrants Purchase Agreement and the DGCL, the Private Placement Warrant Shares will be validly issued, fully paid and non-assessable.

NET Power Inc.

September 15, 2023

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3. Assuming the due issuance and delivery of the Sponsor Conversion Shares in accordance with the provisions of the Opco LLCA, the Charter and the DGCL, the Sponsor Conversion Shares will be validly issued, fully paid and non-assessable.

4. Assuming the due issuance and delivery of the Merger Shares in accordance with the provisions of the Opco LLCA, the Charter and the DGCL, the Merger Shares will be validly issued, fully paid and non-assessable.

5. Assuming the due issuance and delivery of the JDA Shares in accordance with the provisions of the Opco LLCA, the Charter and the DGCL, the JDA Shares will be validly issued, fully paid and non-assessable.

6. The Private Placement Warrants constitute binding obligations of the Company, enforceable against the Company in accordance with their terms.

Our advice on every legal issue addressed in this letter is based exclusively on the internal law of New York and the DGCL (under which the Company is incorporated).

Our opinions expressed above are subject to the qualifications that we express no opinion as to the applicability of, compliance with, or effect of (i) any bankruptcy, insolvency, reorganization, fraudulent transfer, fraudulent conveyance, moratorium or other similar law or judicially developed doctrine in this area (such as substantive consolidation or equitable subordination) affecting the enforcement of creditors’ rights generally, (ii) general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law), (iii) an implied covenant of good faith and fair dealing, (iv) public policy considerations which may limit the rights of parties to obtain certain remedies, (v) any requirement that a claim with respect to any security denominated in other than U.S. dollars (or a judgment denominated in other than U.S. dollars in respect of such claim) be converted into U.S. dollars at a rate of exchange prevailing on a date determined in accordance with applicable law, (vi) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit and (vii) any laws except the internal law of New York and the DGCL. We advise you that issues addressed by this letter may be governed in whole or in part by other laws, but we express no opinion as to whether any relevant difference exists between the laws upon which our opinions are based and any other laws which may actually govern.

This opinion letter speaks as of the time of its delivery on the date it bears. We do not assume any obligation to provide you with any subsequent opinion or advice by reason of any fact about which we did not have knowledge at that time, by reason of any change subsequent to that time in any law covered by our opinion or for any other reason.

NET Power Inc.

September 15, 2023

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This opinion letter is furnished to you in connection with the filing of the Registration Statement and is not to be used, circulated, quoted or otherwise relied upon for any other purpose.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the prospectus included in the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Commission.

Very truly yours,

/s/ KIRKLAND & ELLIS LLP