JEE Mains · Chemistry · STD 11 - 5. Thermodynamics and thermochemistry
The molar heat capacity for an ideal gas at constant pressure is \(20.785\,J\,K ^{-1}\,mol ^{-1}\). The change in internal energy is \(5000\,J\) upon heating it from \(300\,K\) to \(500\,K\). The number of moles of the gas at constant volume is [Nearest integer] (Given: \(R =8.314\,J\,K ^{-1}\,mol ^{-1}\))
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(C _{ p , m }= C _{ v , m }+ R\) \(\Rightarrow C _{ v , m }=20.785-8.314=12.471\,J\,k ^{-1}\,ml ^{-1}\) \(\Delta U = nC _{ r , m } \Delta T\) \(\Rightarrow n =\frac{5000}{12.471 \times 200}=\frac{25}{12.471} \approx 2\)
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