Question

A household refrigerator with a coefficient of performance $1.2$ removes heat from the refrigerated space at the rate of $60kJ/\min$. What would be cost of running this fridge for one month ($30days$)(assuming each day it is used for$4$ hours and cost of one electrical unit is$6Rs.$ )
A. $180Rs.$
B. $300Rs.$
C. $480Rs.$
D. $600Rs.$

Answer 1

As in the given question we know we are given with energy per minute and coefficient of performance and we know the formula $\dfrac{Q}{W} = 1.2$ to calculate the power and then we will calculate for given days and then total cost.

Complete step by step answer:
As in the question we are given with
coefficient of performance as, $1.2$
And energy per minute as, $60kJ/\min$
And total no. of days as, $30days$
And no. of hours it is used in each day as, $4$
And we are also given cost of each unit as, $6Rs.$
So now substituting values in formula we get,
$\dfrac{Q}{W} = 1.2$, where $Q$is energy per unit minute
$\dfrac{{60}}{W} = 1.2$
$W = 50kJ/\min$
$W = 50000J/\min$
$W = \dfrac{{50000}}{{60}}J/\sec$
$W = \dfrac{5}{6}kW$
So now to calculate total power
${W_t} = \dfrac{5}{6} \times 4 \times 30$
${W_t} = 100kWh$, as we have calculated total so now to calculate total cost
$C = 100 \times 6$
$C = 600Rs$
So the correct option is D.

Additional Information:
The coefficient of execution or COP of a warmth siphon, fridge or cooling framework is a proportion of helpful warming or cooling given to work required. Higher COPs liken to bring down working expenses. The COP typically surpasses, particularly in heat siphons, in light of the fact that, rather than simply changing over work to warm, it siphons extra warmth from a warmth source to where the warmth is required. For complete frameworks, COP counts ought to incorporate vitality utilization of all force devouring assistants. COP is profoundly reliant on working conditions, particularly outright temperature and relative temperature among sink and framework, and is regularly arrived at the midpoint of against expected conditions. Performance of Absorption cooler chillers is commonly much lower, as they are not heat siphons depending on pressure, yet rather depend on substance responses driven by heat.

Note: Remember the concept of power and energy and energy per unit time and for coefficient of performance and basic units of electricity that are $kWh$ which we have calculated above in the form of $W$.