# Question #100da

Apr 1, 2015

You can't find the energy with just the information you have given. More information is required but here are a couple of possibilities.

1) If you are submerging an object in a constant temperature water bath for two hours, the object will presumably reach a temperature that is the same as the water bath (thermal equilibrium). If you know this value (say ${60}^{o} C$), the starting temperature (say ${20}^{o} C$), the mass of the object (say 100 g) and its specific heat capacity (say 500 $\frac{J}{g} ^ o C$) then you can figure out the energy supplied $\Delta Q$ using the following equation.

$\Delta Q = m c \Delta T$ where
$\Delta Q = \left(100\right) \left(500\right) \left(60 - 20\right)$

2) If you are putting the object in a water bath and turning it on, then measuring the time it takes to heat to a certain temperature, you could also approximate the energy supplied to the object by the following:

energy supplied to object = energy supplied to water bath - energy required to heat the water

This assumes no heat loss to the surroundings (which if you could measure, you could also subtract out of the above equation).

The energy supplied by any heating appliance can be approximated by calculating the value of $P o w e r \cdot t i m e$ where the power is the wattage rating of the appliance, and the operating time is measured in seconds.

Using this method, the energy supplied to the water bath can be determined, and the energy used to heat the water could be found using the earlier equation.
$\Delta Q = m c \Delta T$ where
m = mass of water in bath
c = SHC of water (4.18 J/gK)
$\Delta T$ = change in temperature

I would highly doubt the accuracy of this calculation due to the heat loss out the top of the water bath.