When two objects P and Q are supplied with the same quantity of heat,the temperature change in P is observed to be twice that in Q. If the masses of P and Q...

When two objects P and Q are supplied with the same quantity of heat,the temperature change in P is observed to be twice that in Q. If the masses of P and Q are the same,calculate the ratio of the specific heat capacities of P and Q

Answer Details

The specific heat capacity of a substance is defined as the amount of heat energy required to raise the temperature of one kilogram of the substance by one degree Celsius. Let the specific heat capacity of object P be Cp and that of Q be Cq, and let their masses be m each. According to the question, the heat supplied to P and Q are the same, let's say Q. So, Heat supplied to P = Heat supplied to Q m × Cp × ΔT_P = m × Cq × ΔT_Q where ΔT_P and ΔT_Q are the temperature changes in P and Q, respectively. We are given that ΔT_P = 2ΔT_Q. Therefore, substituting this into the above equation, we get: m × Cp × 2ΔT_Q = m × Cq × ΔT_Q Cp/Cq = ΔT_Q / ΔT_Q x 2 Cp/Cq = 1/2 Therefore, the ratio of the specific heat capacities of P and Q is 1:2. Hence, the answer is (d) 1:2.