• # question_answer A gas expands adiabatically at constant pressure such that its temperature $T\,\propto \,a/\sqrt{V}.$ The value of $\gamma =({{C}_{p}}/{{C}_{V}})$ of the gas is A) 1.30      B) 1.50 C) 1.67 D) 2.00

 [b] In adiabatic expansion, $p{{V}^{\gamma }}=\,$constant put $p=\,\frac{RT}{V}$ $\left( \frac{RT}{V} \right)\,{{V}^{\gamma }}=\,\,\text{constant}\,\,$ $T{{V}^{\gamma -1}}=$constant or $T\propto \,{{V}^{1-\gamma }}$ $\because$     $T\propto \,\frac{1}{\sqrt{V}}$ $\therefore$    $1-\gamma =-\frac{1}{2}$ or         $\gamma =1+\frac{1}{2}\,=\frac{3}{2}\,=1.5$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://studyadda.com/sample-papers/topic-test-thermodynamical-processes_q18/2568/501658", "fetch_time": 1642751617000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00233.warc.gz", "warc_record_offset": 510300878, "warc_record_length": 21468, "token_count": 241, "char_count": 578, "score": 3.5, "int_score": 4, "crawl": "CC-MAIN-2022-05", "snapshot_type": "latest", "language": "en", "language_score": 0.45633217692375183, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00018-of-00064.parquet"}