Question

When the same quantity of heat is absorbed by a system at two different temperatures T₁​ and T_2​, such that T_1​>T₂​, change in entropies are ΔS_1​ and ΔS₂​ respectively. Then

• A. ΔS₂< ΔS₁
• B. ΔS₁< ΔS₂​
• C. ΔS₁= ΔS₂​
• D. ΔS₂> ΔS₁​

Answer 1

The Correct Option is B

The change in entropy \( \Delta S \) when a certain quantity of heat \( Q \) is absorbed or rejected by a system is given by the formula: \[ \Delta S = \frac{Q}{T} \] where \( T \) is the temperature at which the heat is transferred. Given that the same quantity of heat \( Q \) is absorbed at two different temperatures \( T_1 \) and \( T_2 \), and since \( T_1 > T_2 \), we can compare the changes in entropy: \[ \Delta S_1 = \frac{Q}{T_1}, \quad \Delta S_2 = \frac{Q}{T_2}. \] Since \( T_1 > T_2 \), it follows that: \[ \Delta S_1 < \Delta S_2. \] Thus, the change in entropy is greater at the lower temperature, so \( \Delta S_1 < \Delta S_2 \).

Thus, the correct answer is (B): \( \Delta S_1 < \Delta S_2 \).