Question

How much heat is given off as 25 g of ethanol vapour at ${78^ \circ }C$ is condensed and then cooled to ${15^ \circ }C$?

Answer 1

Whenever heat is added to a system, the temperature of the system increases and vice-versa. However, when there is a transformation in the phase of the object, the heat transfer takes place at constant temperature. This hidden or extra heat is called latent heat.

Complete step by step solution:
The matter undergoes phase transformation from one state to another, involving the transfer of heat energy. The change in phase i.e. solid, liquid or gas to another phase happens at a constant temperature depending on the atmospheric pressure. Here, the heat transfer takes place at constant temperature as opposed to normal cases where heat transfer alters the temperature. Hence, there is an excess amount of heat stored or released during phase transformation. This heat is called latent heat.
When ethyl alcohol loses heat from ${78^ \circ }C$to ${15^ \circ }C$, the formula for the heat transfer is given by –
$H = mc\Delta T$
where m = mass of ethyl alcohol c = specific heat capacity of alcohol $\Delta T$ = change in temperature
Here, we have to also consider the latent heat lost when vapours of ethyl alcohol condense to liquid at the same temperature.
Total heat transferred to atmosphere, $Q = H + L$
where L = latent heat.
The latent heat is given by the formula –
$L = ml$
where $l =$specific latent heat of the substance.
Hence,
$Q = mc\Delta t + ml$
Given,
Mass of alcohol, m = 25 g Temperature change, $\Delta T = 78 - 15 = {63^ \circ }C$ Assuming, Specific heat capacity of ethyl alcohol, c = 2.46 J/g/$^ \circ C$ Specific latent heat of ethyl alcohol, $l = 846kJ - k{g^{ - 1}} = 846J{g^{ - 1}}$
Substituting,
$Q = 25 \times 2 \cdot 46 \times 63 + 25 \times 846$
$\Rightarrow Q = 3874 \cdot 5 + 21150 = 25024 \cdot 5J = 25 \cdot 02kJ$
Total heat given off, by the ethyl alcohol, $Q = 25 \cdot 02kJ$

Note: Steam causes severe boils compared to water at boiling point, even though they are at the same temperature, ${100^ \circ }C$. This is because the steam has a higher amount of heat energy than water at boiling point due to the presence of latent heat of evaporation. The value of specific latent heat considered here for ethyl alcohol is actually, the latent heat of evaporation. The latent heat for condensation is the same as that of the specific latent heat for evaporation but, with a negative sign.