If R = universal gas constant, the amount of heat needed to raise the temperature of 5 mol of an ideal monoatomic gas from 273 K to 373 K when no work is done is :
Answer & explanation
Correct answer: option 1
The correct answer is Option 1: 750 R
Since the question states that no work is done ($W = 0$), the volume of the gas remains constant (isochoric process). In such a process, the heat supplied ($Q$) is equal to the change in internal energy ($\Delta U$).
For an ideal monoatomic gas at constant volume: $Q = nC_v\Delta T$
Where: $C_v$ (Molar specific heat at constant volume) for a monoatomic gas = $\frac{3}{2}R$
Given Values:
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Number of moles ($n$) = $5\text{ mol}$
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Temperature change ($\Delta T$) = $373\text{ K} - 273\text{ K} = 100\text{ K}$
$Q = 5 \times \frac{3R}{2} \times 100$
$Q = 5 \times 1.5R \times 100$
$Q = 750R$