Question

Which uses more energy, a \[250{\text{ }}W\] TV set in \[1{\text{ hr}}\] , or a \[1200{\text{ }}W\] toaster in\[10{\text{ minutes}}\] ?

Answer 1

Hint:The powers of a tv and a toaster are given. Also, the rates are given. The work done by these machines has to be calculated from the given data using the formula of the work done in terms of power. The energy consumed by a machine is equal to the work done by it.

Formula used:
The energy consumed by a machine, $W = Pt$
$P$ is the power of a machine that works for time $t$ .


 Complete step by step solution:
The two machines are given here, a TV of \[250{\text{ }}W\] and a toaster of \[1200{\text{ }}W\].
Let, the power of the TV is \[{P_1} = 250{\text{ }}W\]
And, the power of the toaster is \[{P_2} = 1200{\text{ }}W\]
The tv is running for the time ${t_1} = 1hr = 3600\sec $
And, the toaster is running for the time ${t_2} = 10{\text{minutes}} = 600\sec $
Now, the work done on a machine can be calculated by multiplying the power of the machine and the time(in seconds). This work is the value of the consumption of the energy by the machine.
Hence, The energy consumed by TV, ${W_1} = {P_1}{t_1}$
$ \Rightarrow {W_1} = 250 \times 3600$
$ \Rightarrow {W_1} = 900000{\text{Joule}}$
$ \Rightarrow {W_1} = 9 \times {10^5}{\text{Joule}}$
And, The energy consumed by Toaster, ${W_2} = {P_2}{t_2}$
$ \Rightarrow {W_2} = 1200 \times 600$
$ \Rightarrow {W_2} = 720000{\text{Joule}}$
$ \Rightarrow {W_2} = 7.2 \times {10^5}{\text{Joule}}$
Therefore, from the calculation of energy consumption separately for the TV and Toaster, it is shown that ${W_1} > {W_2}$
Hence, the TV set uses more energy than the toaster.

Note:Work and Energy are the same things.
Work done is denoted in the relationship with the applied force. and, energy is represented by other factors such as heat.
Power is defined as the rate of the work done per unit time. Power is a scalar quantity that doesn’t have any direction. The SI unit of power is Joules/Second, termed as Watt.
Watt can be described as the power needed to do one joule of work in one second.
The unit Watt is named such to give the honor to So James Watt, the developer of the steam engine.