Cost

Calculate how much it costs to take a shower, assuming that $50$ litres of water must be heated from $20$ degrees to $60$ .

How we do it

Our calculation has the following steps:

Calculate how much energy it takes to heat the water (you can do this with a calculator).
Using a calculator, you can work out how much water it takes to heat the water.
We multiply the number of kilowatt-hours by the cost of the electricity per kilowatt-hour using a calculator.

1. Calculate how much energy is needed to heat the water

Calculator: amount of heat during heating and cooling of bodies

The calculator calculates the amount of heat required to heat bodies from a substance or the amount of heat released when they cool down, using the formula $Q = c m Δ t$ . When using the calculator, enter the data in the table. The answer appears in the last row of the table.

Specific heat $c$ of matter	$\frac{J}{^{\circ} C \cdot k g}$
Mass $m$	$k g$
Initial temperature $t_{1}^{\circ}$	$^{\circ} C$
Final temperature $t_{2}^{\circ}$	$^{\circ} C$
Temperature change $Δ t$	$^{\circ} C$
Internal energy change $Q = c m Δ t$	$J$ *

* A negative result indicates that the internal energy of the body decreased. A positive result indicates that the internal energy of the body increased.

The table shows the specific heats of several well-known substances.

2. Convert joules to kilowatt-hours.

Calculator: from kilowatt-hours to joules

Thecalculator converts energy from joules to kilowatt-hours or vice versa, where $1 k W h = 3.6 \times 10^{6} J$ . When using the calculator, enter the data in the table, the answer will appear in the last row of the table.

$J \to k W h$

Energy $J$
Energy $k W h$

$k W h \to J$

Energy $k W h$
Energy $J$

3. We multiply the number of kilowatt-hours by the cost of electricity per kilowatt-hour.

Calculator: cost of electricity

Thecalculator calculates theprice of electricity consumed using the formula $H = Q [k W h] \cdot H_{kWh} [\frac{E U R}{k W h}]$ . When using the calculator, enter the data in the table. The answer will appear in the last row of the table.

Energy used $Q$	$k W h$
Energy cost $H_{kWh}$	$\frac{E U R}{k W h}$
Price of electricity $H = Q \cdot H_{kWh}$ $	$E U R$

Electricity exchange price today and tomorrow

On this page you can view the electricity exchange price in real time and the electricity price today and tomorrow by the hour.

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Answer

The cost of one shower under such conditions is (EUR)

So: all those who thought that one of these moves would cost less than an ice-cream were right.

But let's calculate some more such everyday prices below. All the calculators can be reused, i.e. you just have to enter new input values to get new results.

The situation	Price (EUR)
Boil a 1 liter jug of water.
A car weighing $1,200 is brought into a garage with $20 h e a t p l u s$ 20 from sub-zero temperatures in the winter.
The water resources of Võrtsjärvi reach 750,000 thousand cubic meters of water. We want to raise the temperature of this water by one degree.

How big a chunk of oil shale would have to be burned to make it possible for someone to take a shower?