An object with a mass of #1 kg#, temperature of #150 ^oC#, and a specific heat of #24 J/(kg*K)# is dropped into a container with #27 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?

1 Answer
Dec 16, 2017

Answer:

The water does not evaporate and the change in temperature is #=0.036^@C#

Explanation:

The heat is transferred from the hot object to the cold water.

Let #T=# final temperature of the object and the water

For the cold water, # Delta T_w=T-0=T#

For the object #DeltaT_o=150-T#

# m_o C_o (DeltaT_o) = m_w C_w (DeltaT_w)#

The specific heat of water is #C_w=4.186kJkg^-1K^-1#

The specific heat of the object is #C_o=0.024kJkg^-1K^-1#

The mass of the object is #m_0=1kg#

The mass of the water is #m_w=27kg#

#1*0.024*(150-T)=27*4.186*T#

#150-T=(27*4.186)/(1*0.024)*T#

#150-T=4186T#

#4187T=150#

#T=150/4187=0.036^@C#

As #T<100^@C#, the water does not evaporate