Thermal Physics (Specific Heat Capacity)

[Tikiboom1]

Homework Statement

Body X whose temperature is 0 °C is brought into thermal contact with body Y of equal mass and temperature 100 °C. The only exchanges of heat that take place are between X and Y. The specific heat capacity of X is greater than that of Y. Which statement about the final equilibrium temperature T of the two bodies is correct?

A) T = 50 °C
B) 0 < T < 50 °C
C) 100 °C > T > 50 °C
D) Answer depends on value of mass

Homework Equations

E = MCΔt

The Attempt at a Solution

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Let the specific heat capacity (SHC) of X to be Cx and SHC of Y to be Cy.

Since the only heat exchange is between X and Y, the heat lost by body Y = heat gained by body X.

Therefore, we know Cx > Cy and MCxΔt = MCyΔt

Since the masses are equal we can cancel them off. We can also find an equation for Δt based of it's initial temperatures as stated above and it's final equilibrium temperature (T).

Therefore, Cx(T) = Cy(100-T)

We can rearrange to give Cx/Cy = (100-T)/(T). Since Cx>Cy, we can deduce that 100-T>T.

This gives the final equation 100 > 2T and finally 50 > T.

So the answer should be B) 0 < T < 50. However, the answer given in the book is A) T = 50°C. I can't tell where I've gone wrong during my working out? Logically, my answer B) seems to make sense too. If the SHC of X is more than Y, then it takes more energy to raise X by 1°C compared to Y. Therefore, the energy lost by Y when the temperature decreases by 1°C is less than the amount required by X to increase by 1°C. Therefore, for every 1°C of temperature body Y drops, body X will gain less than 1°C. Is the answer in the textbook wrong?

 

[Bystander]

You are correct; the book is wrong, if the problem is copied correctly.