An object with a mass of #3 kg#, temperature of #210 ^oC#, and a specific heat of #24 J/(kg*K)# is dropped into a container with #36 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?

Question

An object with a mass of #3 kg#, temperature of #210  ^oC#, and a specific heat of #24 J/(kg*K)# is dropped into a container with #36  L # of water at #0^oC #.  Does the water evaporate?  If not, by how much does the water's temperature change?

Isabella Alvarez · Accepted Answer

The water will not evaporate and the change in temperature is #=0.1^@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=210-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=3kg#

The mass of the water is #m_w=36kg#

#3*0.024*(210-T)=36*4.186*T#

#210-T=(36*4.186)/(3*0.024)*T#

#210-T=2093T#

#2094T=210#

#T=210/2094=0.1^@C#

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

Charlotte Aaron · Answer

undefined To determine if the water evaporates, we first calculate the heat gained or lost by the water using the formula $Q = mcΔT$, where $Q$ is the heat transferred, $m$ is the mass of the water, $c$ is the specific heat capacity of water, and $ΔT$ is the change in temperature. Then, we compare this amount of heat to the heat required for the water to evaporate, which is the heat of vaporization ($Q_{\text{vap}}$). If $Q_{\text{water}} < Q_{\text{vap}}$, the water does not evaporate; otherwise, it does.

Given that the mass of water is $36 \, \text{L}$ (which we'll need to convert to kg), $c = 4186 \, \text{J/(kg*K)}$ (specific heat capacity of water), and $ΔT$ is the change in temperature of water. To calculate $ΔT$, we rearrange the equation as $ΔT = \frac{Q}{mc}$. $Q$ can be calculated using the given mass, temperature change, and specific heat capacity of the object.

Once we find $ΔT$, we check if $Q_{\text{water}} < Q_{\text{vap}}$ to determine if the water evaporates. If not, we know the water's temperature change is equal to $ΔT$.