When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

# When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

1. A

$\frac{2}{5}$

2. B

$\frac{3}{5}$

3. C

$\frac{3}{7}$

4. D

$\frac{5}{7}$

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### Solution:

$dQ=dU+dW$

$\frac{dQ}{dQ}=\frac{dU}{dQ}+\frac{dW}{dQ}$

$\frac{dU}{dQ}=1-\frac{dW}{dQ}=1-\frac{nRdT}{n{c}_{p}dT}=\frac{{c}_{v}}{{c}_{p}}=\frac{1}{\gamma }$

diatomic $\gamma =\frac{7}{5}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\frac{dU}{dQ}=\frac{5}{7}$

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