When two objects P and Q are supplied with the same quantity of heat, the...

JAMB 2017

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 of Q. The mass of P is half that of Q. The ratio of the specific heat capacity pf P to Q is

A. 1:4
B. 4:1
C. 1:1
D. 2:1

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Correct Answer: Option C

Explanation

H = mcθ

H_P = H_Q, θ_P = 2θ,

m_P = \(\frac{1}{2}\)m_Q

∴ H_P = m_QC_Pθ_P, also HQ = m_QC_Qθ_Q

Since H_P = H_Q

∴ m_Pc_Pθ_P = m_Qc_Pθ_q

Putting in the conditions

\(\frac{1}{2}\)m_Q × c_P × 2θ_Q = m_Q × θ_Q × c_Q

∴ c_P = c_Q

\(\frac{C_p}{C_Q}\)= \(\frac{1}{1}\)

= 1:1

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