Discussion
One mole of a monoatomic gas is heated at constant volume such that its temperature increases from \(T\) to \(3T\) . The heat supplied is (\(R\)- Universal Gas constant)
Answer: A
The heat supplied is \(3RT\).
At constant volume no work is done, and for a monatomic gas \(C_{V} = \frac{3}{2}R\) per mole:
\[ \begin{aligned} Q &= nC_{V}\Delta T = 1 \times \tfrac{3}{2}R \times (3T - T) \\ &= 3RT \end{aligned} \]
\(\frac{3}{2}RT\) forgets that the rise is \(2T\), not \(T\). \(5RT\) uses \(C_{P} = \frac{5}{2}R\), which applies at constant pressure.
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