dQ is the heat energy supplied to an ideal gas under isochoric conditions. If $\mathrm{dU}$ and…

dQ is the heat energy supplied to an ideal gas under isochoric conditions. If $\mathrm{dU}$ and $\mathrm{dW}$ denote the change in internal energy and the work done respectively then
  1. $\mathrm{dQ}=\mathrm{dW}$
  2. $\mathrm{dQ}>\mathrm{dU}$
  3. $\mathrm{dQ} < \mathrm{dU}$
  4. $\mathrm{dQ}=\mathrm{dU}$

Solution

Under isochoric (constant volume) conditions, the heat energy (dQ) supplied to an ideal gas contributes solely to the change in its internal energy (dU). Mathematically, this can be expressed as $\begin{aligned} & \mathrm{dQ}=\mathrm{dU}+\mathrm{dW} \\ & \Rightarrow \mathrm{dQ}=\mathrm{dU} \end{aligned}$

Asked in: MHT CET 2023 (13 May Shift 1)

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