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An object with a mass of #24 kg#, temperature of #270 ^oC#, and a specific heat of #8 J/(kg*K)# is dropped into a container with #48 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?

Answer 1

Leo Abeyta

The water does not evaporate and the change in temperature is #=0.26^@C#

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=270-T#

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

The specific heat of the object is #C_o=0.008Jkg^-1K^-1#

The mass of the object is #m_0=24kg#

The volume of water is #V=48L#

The density of water is #rho=1kgL^-1#

The mass of the water is #m_w=rhoV=48kg#

#24*0.008*(270-T)=48*4.186*T#

#270-T=(48*4.186)/(24*0.008)*T#

#270-T=1046.5T#

#1047.5T=270#

#T=270/1047.5=0.26^@C#

As the final temperature is #T<100^@C#, the water will not evaporate.

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Answer 2

Julia Aguilar

The water does not evaporate. The temperature of the water increases by approximately 0.0094 degrees Celsius.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.