JEE PYQ: Thermodynamics Question 33
Question 33 - 2019 (09 Apr Shift 2)
A massless spring (K = 800 N/m), attached with a mass (500 g) is completely immersed in 1kg of water. The spring is stretched by 2cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)
(1) $10^{-4}$ K
(2) $10^{-5}$ K
(3) $10^{-1}$ K
(4) $10^{-3}$ K
Show Answer
Answer: (2)
Solution
$\frac{1}{2}kx^2 = mC(\Delta T) + m_w C_w \Delta T$
$\frac{1}{2} \times 800 \times 0.02^2 = 0.5 \times 400 \times \Delta T + 1 \times 4184 \times \Delta T$
$\therefore \Delta T = 1 \times 10^{-5}$ K
BETA
