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KCET · Physics · Thermodynamics

\(310 \mathrm{~J}\) of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from \(25^{\circ} \mathrm{C}\) to \(35^{\circ} \mathrm{C}\). The amount of heat required to raise the temperature of the gas through the same range at constant volume is

  1. A \(384 \mathrm{~J}\)
  2. B \(144 \mathrm{~J}\)
  3. C \(276 \mathrm{~J}\)
  4. D \(452 \mathrm{~J}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(144 \mathrm{~J}\)

Step-by-step Solution

Detailed explanation

At constant pressure,
Heat required \(=n C_{p} \Delta T\)
\(\Rightarrow 310=2 \times C_{p} \times(35-25)\)
\(\Rightarrow C_{p}=\frac{310}{20}=15.5 \mathrm{~J} / \mathrm{mol} / \mathrm{K}\)
Similarly, at constant volume,
Heat required \(=n C_{V} \Delta T\)
\(=2\left(C_{p}-R\right) \times(35-25)\)
\(\left[\because C_{p}-C_{V}=R\right]\)
\(=2 \times(15.5-8.3) \times 10\) \(=2 \times 7.2 \times 10=144 \mathrm{~J}\)
\(=2 \times 7.2 \times 10=144 \mathrm{~J}\)