Heat and temperature

Classical Mechanics Level 1

There are two pots(with water) A and B with mass $m_1$ and $m_2$ . Equal amount of heat is getting produced to both pots. Given that the temperature of A and B is $T_1$ and $T_2$ . What will be the relation between $T_1$ and $T_2$ if $m_1 > m_2?$

Note: The initial temperature of both pots is 0.

T_1 = T_2

T_1 > T_2

T_1 < T_2

1 solution

Denis Kartachov
Aug 21, 2018

Assume for the sake of simplicity, the initial temperature of both pots to be $T_0 = 0$ so the reference internal energy will also be $U_0 = 0$ , then the thermodynamic relationship for the change in internal energy holds (since no work is being done):

$U = mc_pT$

Where $c_p$ is the constant pressure specific heat of water (same in both pots assuming atmospheric pressure). If equal amounts of heat is added to both pots, the internal energy also changes accordingly, so we have:

$m_1 T_1 = m_2 T_2$

Where $c_p$ cancels out. Rearranging:

$\frac{m_1}{m_2} = \frac{T_2}{T_1}$

If $m_1 > m_2$ or $\frac{m_1}{m_2} > 1$

This implies

$\frac{T_2}{T_1} > 1$

And thus $T_2 > T_1$ the temperature in pot B has to be higher.

Heat and temperature

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