# Equilibrium temperature of closed system

Body X of temperature 0° C is brought into thermal contact with body Y of temperature 100° C. X has specific heat capacity higher than of Y. The masses of X and Y are equal.

By my reasoning, the final equilibrium temperature should lie between 0° C and 50° C. Is this correct?

Edit: 1) The bodies are in thermal contact only with one another; they are in a closed system.

2) My reasoning:

$Q_x=m_xc_x\Delta T_x$

$Q_y=m_yc_y\Delta T_y$

$Q_x=Q_y$, $m_x=m_y$

$c_x\Delta T_x=c_y\Delta T_y$

If $c_x$ is higher than $x_y$, then $\Delta T_x$ must be lower thab $\Delta T_y$, so the equilibrium temperature must lie below 50° C.

• Please, be more specific and elaborate the question a bit more. What is the enviroment and surroundings of bodies? What is your arguments? Nov 18, 2015 at 11:13

That's an intuitive guess but you should get some good proof to support your argument.

Better is to apply the principle of calorimetry to get a firm grip on your answer and reasoning:

if two substances of different temperature are in thermal contact and if no heat is allowed to go out or enter into and if no chemical reactions takes place in between the two bodies then heat lost by the hotter body will be equal to the heat gained by the colder body.i.e.heat lost=heat gained

Say if $T$ is the final temperature, from the equation you obtain, check what you can comment on the range of $T$.

• See edit for my calorimetric reasoning. However, the answer given is that the equilibrium temperature is 50° C. IS this wrong, or is my explanation wrong? Nov 18, 2015 at 11:25
• @Marcel Put the values of $\Delta T_x$ and $\Delta T_y$ i.e. $T-0$ and $100-T$. See what you get. You will yourself realise if you are correct or not. Nov 18, 2015 at 11:28
• That gives $C_x \Delta T+C_y \Delta T = C_y100$, but I don't see how that helps Nov 18, 2015 at 11:43
• Your $T$ strictly depends on the values of $c_x$ and $c_y$. Put values and check. You hence cannot comment on the range of $T$, or can you? Nov 18, 2015 at 12:37