Question

unknown object has a mass of 20kg and a specific heat of 5 kg-1 K-1. The object is heated to 350K and then placed in a bucket containing 50L of water initially at 300K. If the bucket is a perfect insulator, with negligible heat capacity, what is the final temperature of the water after thermal equilibrium has been established?

Answer 1

Solution :

Given :

Mass of the unknown object : m = 20 kg

Specific heat : C = 5 J kg^-1 K^-1

*** { I think this given quantity is not complete. If the given value is not correct. Please follow the whole process using the actual value. Remaining values will remain same}

Initial temperature : T_i = 350 K

.

And, Volume of water : V = 50 L

So, Mass of the water : m_w = 50 kg

Specific heat of water : Cw = 4186 J kg^-1 K^-1

Initial temperature of water : T_w = 300 K

.

Let the final temperature be T_f.

Then, According to conservation of energy. When the thermal equilibrium is established :

Heat lost by the unknown object = Heat gained by water

∴ m C (T - T_f) =  m_w C_w (T_f - T_w)

∴ (20)(5)(350 - T_f) = (50)(4186)(T_f - 300)

∴ 35000 - (100)T_f = (209300)T_f - (62790000)

∴ (209400)T_f = 62825000

∴ T_f = 300.024 K