What is the difference between specific heat and heat capacity? If you heat 500g of H2O initially at 8C in a 1000 W microwave with 80% efficiency for 2 minutes, what will the final temperature be?
specific heat has units of J/g*K or joules/gram/degree kelvin. Typically, specific heat is the heat required to raise the temperature of 1 gram of some material by 1 degree K. Heat capacity has units of J/K; i.e., note no "specificity" in amount as in grams. There is a good discussion here.
http://en.wikipedia.org/wiki/Heat_capacity
For the problem, 1 watt is 1J/s. You have 1000 watts so it is 1000 J/s. You run it for 2 minutes which = 1000 x 2 x (60 s/min) = ?. It is only 80% efficient; therefore, ? x 0.8 = q = heat produced.
Then q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Use 4.184 J/g*C for specific heat H2O unless you are given some other number.
Specific heat and heat capacity both refer to the amount of heat energy required to change the temperature of a given substance. However, they differ in terms of the quantity being considered.
Specific heat (symbol: c) is the amount of heat energy required to raise the temperature of one unit of mass (usually one gram or one kilogram) of a substance by one degree Celsius (or one Kelvin). It is expressed in units of J/g·°C or J/kg·K.
Heat capacity (symbol: C) is the amount of heat energy required to raise the temperature of a given quantity of a substance by one degree Celsius (or one Kelvin). It is calculated by multiplying the specific heat of the substance (c) by its mass (m). Heat capacity is expressed in units of J/°C or J/K.
Now, let's calculate the final temperature of the water after heating it in the microwave.
To solve this problem, we can use the equation:
Q = mcΔT
where:
Q = heat energy (in Joules)
m = mass of the substance (in grams)
c = specific heat of the substance (in J/g·°C)
ΔT = change in temperature (in °C)
We are given:
m = 500g (mass of water)
c = 4.18 J/g·°C (specific heat of water) [Note: This value is approximate and can vary slightly with temperature.]
ΔT = final temperature - initial temperature = final temperature - 8°C
We know that the microwave has an 80% efficiency, meaning only 80% of the energy is absorbed by the water.
The power (P) of the microwave is given as 1000 W, and the time (t) is 2 minutes (or 120 seconds). Using the equation for power (P = W/t), we can calculate the energy (W) absorbed by the water:
W = Pt = 1000 W * 120 s = 120,000 J
Since the efficiency is 80%, the actual energy absorbed by the water is:
Actual energy absorbed = 80% of 120,000 J = 0.8 * 120,000 J = 96,000 J
Now, we can substitute the values into the equation Q = mcΔT:
Q = 96,000 J
m = 500 g
c = 4.18 J/g·°C
ΔT = final temperature - 8°C
Now, we can rearrange the equation to solve for the final temperature:
Q = mcΔT
ΔT = Q / (mc)
ΔT = 96,000 J / (500 g * 4.18 J/g·°C)
ΔT ≈ 45.91 °C
Finally, adding the change in temperature to the initial temperature:
Final temperature = 8°C + ΔT ≈ 8°C + 45.91°C ≈ 53.91°C
Therefore, the final temperature of the water after heating for 2 minutes would be approximately 53.91°C.