• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q. 3.12

Expert-verified Found in: Page 97 ### An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279 # Estimate the change in the entropy of the universe due to heat escaping from your home on a cold winter day.

The entropy change on a cold winter day can be estimated to be $8.0×{10}^{4}\mathrm{J}/\mathrm{K}$.

See the step by step solution

## Step 1: Given

It is given to estimate the change in the entropy of the universe due to heat escaping from your home on a cold winter day.

Hence,

Let's assume:

Power consumed from an average house on a winter day $=P=4kW=4×{10}^{3}J/s$

Temperature inside $={T}_{in}=293K$

Temperature outside $={T}_{out}=275K$

## Step 2: Calculation

Total heat loss in a day can be calculated as:

$Q=Pt$

Where,

$P$ = Power

$t$ = time

Hence,

$Q=4×{10}^{3}×24×60×60\phantom{\rule{0ex}{0ex}}Q=3.46×{10}^{8}J$

Now,

Entropy gained by outdoors can be given as:

$\Delta {S}_{\text{out}}=\frac{Q}{{T}_{\text{out}}}$

By substituting the values, we get,

$\Delta {S}_{\text{out}}=\frac{3.46×{10}^{8}}{275}\phantom{\rule{0ex}{0ex}}\Delta {S}_{\text{out}}=1.26×{10}^{6}\mathrm{J}/\mathrm{K}$

And,

Entropy gained by indoors can be given as:

$\Delta {S}_{in}=-\frac{Q}{{T}_{in}}$

By substituting the values, we get,

$\Delta {S}_{\text{in}}=-\frac{3.46×{10}^{8}}{293}\phantom{\rule{0ex}{0ex}}\Delta {S}_{in}=-1.18×{10}^{6}\mathrm{J}/\mathrm{K}$

We know that the net entropy change is given as:

$\Delta {S}_{net}=\Delta {S}_{out}+\Delta {S}_{\text{in}}$

By substituting the calculated values in the above equation, we get,

$\Delta {S}_{\text{net}}=\left(1.26×{10}^{6}\right)-\left(1.18×{10}^{6}\right)\phantom{\rule{0ex}{0ex}}\Delta {S}_{\text{net}}=8.0×{10}^{4}J/K$

Hence, the required entropy change can be calculated as $8.0×{10}^{4}J/K$. ### Want to see more solutions like these? 