Question

One mole of an ideal gas requires 207 J heat to raise the temperature by 10K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10K, the heat required is (R$=$8.3 J/mol-K)

• A. 187J
• B. 29J
• C. 215.3J
• D. 124 J

Answer 1

The correct option is D 124 J

At constant pressure,
Q = $n{C}_p\Delta T$
207 = $C_p\times 10$
$C_p=20.7$
At constant volume, W = 0
Q = U = $n{C}_v\Delta T$
$C_p=C_v+R$
$C_v=20.7-8.3=12.4$
Q = $12.4\times 10$
Q = 124 J