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Physics

Heat

Easy

Question

A tyre pumped to a pressure 3.375 atm at 27^oC suddenly burts. What is the final temperature $left parenthesis gamma equals 1.5 right parenthesis ?$

27 °C
-27 °C
0°C
-73°C

The correct answer is: -73°C

$T subscript 1 superscript 1 minus gamma end superscript P subscript 1 superscript 1 minus gamma end superscript equals T subscript 2 superscript gamma P subscript 2 superscript 1 minus gamma end superscript open parentheses T subscript 1 over T subscript 2 close parentheses to the power of gamma equals open parentheses P subscript 1 over P subscript 2 close parentheses to the power of gamma minus 1 end exponent equals open parentheses 300 over T subscript 2 close parentheses to the power of 3 divided by 2 end exponent equals open parentheses fraction numerator 3.375 over denominator 1 end fraction close parentheses to the power of 3 divided by 2 minus 1 end exponent T subscript 2 equals fraction numerator 300 over denominator left parenthesis 3.375 right parenthesis to the power of 1 divided by 3 end exponent end fraction equals 200 straight K equals negative 73 to the power of ring operator straight C$

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