Question

) 1.3kg of gold at 300K comes in thermal contact with 2.1kg copper at 400K. The specific heats of Au and Cu are 126 J/kg-K and 386 J/kg-K respectively. What equilibrium temperature do they reach

Answer 1

Answer: Equilibrium temperature they reach is 383 K

Explanation:

$heat_{absorbed}=heat_{released}$

As we know that,  

$Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})$

$m_1\times c_1\times (T_{final}-T_1)=-[m_2\times c_2\times (T_{final}-T_2)]$         .................(1)

where,

q = heat absorbed or released

$m_1$ = mass of gold = 1.3 kg

$m_2$ = mass of copper = 2.1 kg

$T_{final}$ = final temperature = ?

$T_1$ = temperature of gold= 300 K

$T_2$ = temperature of copper = 400 K

$c_1$ = specific heat of gold = $126J/kgK$

$c_2$ = specific heat of copper = $386J/kgK$

Now put all the given values in equation (1), we get

$1.3\times 126\times (T_{final}-300)=-[2.1\times 386\times (T_{final}-400)]$

$T_{final}=383K$

Thus equilibrium temperature they reach is 383 K