# 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

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