Question

$310J$ of heat is required to raise the temperature of $2$ moles of an ideal gas at constant pressure from ${25}^{0}C$ to ${35}^{0}C$. The amount of heat energy required to raise the temperature of the gas through the same range at constant volume is

• A. $452J$
• B. $276J$
• C. $144J$
• D. $384J$

Answer 1

Answer: (C)

$144J$

Heat = moles(no.) $\times C_P\times △T$

$\Rightarrow 310=2\times C_P\times 10[35-25=10]\Rightarrow C_P=15.5J/molK$

$\therefore C_P-C_V=R\Rightarrow C_V=C_P-R=15.5-8.314\Rightarrow C_V=7.186J/molK$

$Q=n{C}_V△T=2\times 7.186\times 10=143.72J\approx 144J$