Question

You buy a portable electric heater that claims to put out 10,000 BTUh of heat. Assume it’s 100% efficient at converting electrical energy from the wall outlet to the heat output of the heater. a) Is there anything wrong with the stated units of the heat output? b. What is the electrical energy-consumption rate in watts (W)?

Answer 1

We have rate of heat energy output of given portable electric heater

= H= 10000 BTUh

a)

No there is nothing wrong with the stated unit (BTUh) for heat eneegy output of heater

Here BTU stands for "British Thermal unit" and BTUh stands for "British Thermal Units per hour"

Where,

$1\:BTU=1055.056\:J(joule)$

Therefore,

$1\:BTUh=1055.056\:J/hour$

That is,

$1\:BTUh=\frac{1055.056\:J}{1\:hour}$

Using $1\:hour=60\times60=3600\:s\:(seconds)$ we get,

$1\:BTUh=\frac{1055.056\:J}{3600\:s}$

$1\:BTUh=0.293071\:J/s$

Using $1\:W\:(watt)=1\:J/s$ we get,

$1\:BTUh=0.293071\:W$

b)

We have,

Efficiency of given electric heater = 100 %

That is, heater converts all the input electric energy to heat energy without any loss of energy.

Therefore we get,

consumption rate of input electric energy = rate of output of heat energy ( H )

Therefore,

Consumption rate of input electric energy = H = 10000 BTUh

Now using above conversion factor 1 BTUh = 0.293071 W we get,

Consumption rate of input electric energy $=10000\times0.293071\:W$

There we have,

Consumption rate of input electric energy ( in watts ) $=2930.71\:W$