Question

Two substances, A and B, have the same mass. Substance A is at a higher temperature than B, and heat transfers between them until equilibrium is reached. The decrease in the temperature of A is less than the increase in temperature of B. Which substance has the larger specific heat?

Answer 1

we know that specific heat of a substance is amount of heat needed to increase the temperature of the substance by 1 degree celsius.

let specific heat of substance A and B are s₁ and s₂ respectively.

initial temperature of substance A and B are T₁ and T₂ respectively.

given that initial temperature of substance A is greater then temperature of substance B.

so, T₁  T₂

_{given that mass of both substance is equal ( let m ).}

_{we know that when two substance at different temperatures are kept in contact with each other then heat will transfer from substance at larger temperature to substance at lower temperature until they both reach to a constant final temperature. this final temperature is know as equilibrium temperature of the two body system ( let T be the equilibrium ). and after this process no further heat will be flow from any substance to another substance.}

in this process temperature of A will decrease to final temperature T and temperature of B will increase to final temperature T .

so, we can write that heat energy is transfer from substance A to substance B.

so, heat given by substance A equal to Q=ms₁T = ms₁ (T₁-T)

heat accepted by substance B equal to Q=ms₂ T= ms₂ (T-T₂ )

so , equating them

ms₁ (T₁-T) = ms₂ ( T-T₂)

we know that final temperature T is less then T₁ and greater then T₂.

so, T₂TT₁

now,

s₁ /s₂= (T-T₂ )/(T₁-T)

now, given that decrease in temperature of A (T₁-T) is less then increase in temperature of B ( T-T₂)

so, (T₁-T)( T-T₂)

so, s₁/s₂1

so, s₁s₂

so, substance A has larger specific heat.