KCET · Physics · Kinetic Theory of Gases
One mole of \( 4 \) gas is heated at constant pressure starting at \( 27{ }^{\circ} \mathrm{C} . \) How much energy must be added to the gas as heat to double its volume?
- A \( 750 \mathrm{R} \)
- B Zero
- C \( 1050 \mathrm{R} \)
- D \( 450 \mathrm{R} \)
Answer & Solution
Correct Answer
(C) \( 1050 \mathrm{R} \)
Step-by-step Solution
Detailed explanation
(C)
At constant pressure it volume is doubled, temperate gets doubled,
\( T_{1}=300 \mathrm{k}, T_{2}=600 \mathrm{k} \)
hence \( \Delta T=600-300=300 \mathrm{k} \)
\( Q=n c_{p} \Delta T=1 \times \frac{7}{2} R \times 300=1050 R \)
At constant pressure it volume is doubled, temperate gets doubled,
\( T_{1}=300 \mathrm{k}, T_{2}=600 \mathrm{k} \)
hence \( \Delta T=600-300=300 \mathrm{k} \)
\( Q=n c_{p} \Delta T=1 \times \frac{7}{2} R \times 300=1050 R \)
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