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The specific heat capacity of an object A is X. It is kept in contact with another object B of twice the mass and specific heat capacity of twice of X. If the initial temperature of A  is 100 ° C and B is 200 ° C, what will be change in the temperature of A?

The specific heat capacity of an object A is X. It is kept in contact with another object B of twice the mass and specific heat capacity of twice of X. If the initial temperature of A  is 100 ° C and B is 200 ° C, what will be change in the temperature of A? Correct Answer 60 K

Concept:

  • Specific Heat Capacity: Specific heat capacity is the energy required to increase the temperature of the material of a certain mass by 1°C.
    • SI unit is J/ (kg·K).
  • Heat gained by X = Heat lost by Y

H = m c ΔT, Where m = mass, c = specific heat capacity, ΔT = temperature change.

  • When two objects are kept close, heat is transferred takes place from a hotter body to a cooler one. 
  • Finally, both objects reach the equilibrium temperature. 


Calculation:

The specific heat of A = X

Mass of A = m (let)

Temperature of X = T1 = 100 °C = 373 K

specific heat of B = Y 

Mass of B = 2 m ( twice of A )

Specific heat of A = 2 X (twice of X)

Temperature of  Y = T2 = 200 ° C = 473 K

Let the equibrium temperature be T

Then 

Heat lost by B = Heat gain by A

Heat lost of B = 2 m (2X) (T2 - T) = 4 m X (473 K - T)

Heat gain by A = m X (T - T2) = m X (T - 273K)

Equating

4 m X (473 - T) = m X (T - 273K)

⇒ 4 × 473 - 4 T = T - 273 K

⇒  -5 T = -273 -  4 × 473 = - 2165 K

⇒ T = 433 K

This is the equilibrium temperature. 

The change in temperature = (T - T1) = 433 K - 373 K = 60 K

So, the change in temperature of X = 60 K.

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