Heat Capacity - Video Tutorials & Practice Problems
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Heat Capacity is the amount of heat required to change the temperature of a substance.
Understanding Heat Capacity
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concept
Heat Capacity
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So when we talk about heat capacity, we're talking about, the application of heat to a substance. We're gonna say as we heat an object, its temperature increases because heat is directly proportional to its temperature change. The more heat I apply to something the greater the temperature change will be. So here to illustrate that we say that q being directly proportional to delta t. So just remember, that is the relationship between heat and temperature.
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example
Heat Capacity Example 1
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Here it says if the temperature of a water bath goes from 25 Kelvin to 50 Kelvin, what can be said about the amount of heat? So remember we said that heat, which is q, is directly proportional to change in temperature. Here our temperature is going from 25 Kelvin to 50 kelvin, so it is being doubled in terms of kelvin. And since they're directly proportional, what happens to 1 happens to the other. With our temperature doubling, that would mean that my heat would also have to double. This means that option a would be our correct answer.
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concept
Heat Capacity
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Now heat capacity which uses capital c is the amount of heat required to change the temperature of a weighted substance. The more heat that's applied to a substance, the greater its temperature change. Now it can be looked at also in terms of specific heat capacity and molar heat capacity. With specific heat capacity we lose we use lowercase c, and it is the amount of heat required to change the temperature of 1 gram of a substance by 1 degree. That degree can be either in Kelvin or degrees Celsius. Here, molar heat capacity is just like heat capacity in terms that it be being a capital c. But here with molar heat capacity, it's the amount of heat required to change the temperature of 1 mole of a substance by 1 degree, either in Kelvin or degrees Celsius. Okay? So think of molar heat capacity as being a little bit more, focused in terms of the way we look at heat capacity, in terms of 1 mole of a substance. Now we're going to say here that when it comes to molar heat capacity, which is capital c, it equals q over n times delta t. So capital c equals our molar heat capacity in joules over moles times degrees Celsius or in Kelvin. Q represents heat, t equals temperature in degrees Celsius. But what we need to realize here is that whatever the units that the molar heat capacity uses for temperature, temperature should match it. K? So if this happened to be in Kelvin then temperature should be in Kelvin. And then n is equal to our moles. With our specific heat capacity, it uses lower case c, it equals q over m times delta t. Here lower case c is our specific heat capacity in in joules over grams times degrees Celsius or Kelvin. Q again is heat. Temperature again can be in Celsius or in Kelvin. To determine which one to use, you look at the units for your specific heat capacity and make sure they match. And then lowercase m here is just grams of our substance. So just remember the difference between molar heat capacity and specific heat capacity.
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example
Heat Capacity Example 2
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Here the example says, if 15.7 grams silver raises its temperature by 17.2 degrees Celsius when it absorbs 6,845.5 joules, what is its molar heat capacity? So molar heat capacity uses capital c. It's equal to heat, which is q divided by moles n times change in temperature. In the question it says that we're absorbing this much energy. That means that that's a positive q. So that's positive 6,845.5 joules. Next, we need moles, and we already have the change in temperature. They said that the temperature was, risen by 17.2 degrees Celsius. So that's already our change in temperature. We need moles, we have here 15.7 grams of silver which is a g. We have to change that to moles, so one mole of silver weighs 107.87 grams according to the periodic table. So that comes out to be 0.145548 moles of silver. Take those moles and plug it in. So when we do that that's gonna give me my molar heat capacity as 273 4.45 joules over moles times degrees Celsius. If we look at our values, this has 3 sig figs and this has 3 sig figs, so I could change this to 2.73 times 10 to the 3 joules over moles times degrees Celsius. So that would be the molar heat capacity for silver under these conditions.
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concept
Heat Capacity
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Now by rearranging the specific heat capacity given above, we can solve for the amount of heat released or absorbed. Here our new specific heat capacity formula becomes q equals m times c times delta t. For all of you pre med track students, we usually say that this is equal to q equals mcat, and we know that the mcat is an important exam before you matriculate into medical school. So use that to help you remember it. So q equals mcat is our new formula to help us determine and relate the specific heat capacity to the amount of heat absorbed or released in a chemical reaction.
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example
Heat Capacity Example 3
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Here it says, how much heat in kilojoules is released when 120 grams of water goes from 90 degrees Celsius to 45 degrees Celsius. The specific heat capacity of water is given as 4.184 joules over grams times degrees Celsius. So So we need to determine the heat which is q, they're giving us here the mass of the water which is m, we have our change in temperature here, and we have our specific heat capacity which is lowercase c. So q equals m cap, plug in the grams of water given to us, plug in the specific heat capacity that's given to us, and remember the units for this specific heat capacity dictate the units for temperature. Since this is in Celsius it's good to have our temperatures in Celsius as well. Delta t is final minus initial. So when we do all that, Celsius cancel out, grams cancel out, and we'll have joules of heat involved. When we plug that in, we're gonna get here negative 22593 0.6 joules. But here we want the answer in kilojoules, so 1 kilojoule is equal to 10 to the 3 joules. So here joules cancel out and we'll have kilojoules at the end. So that comes out to negative 22 0.5936 kilojoules. Here, this has 4 sig figs, 1 sig fig, 2 sig figs. Specific heat capacity we could use it since it's given to us as a value, but we don't have to. Here we could just go with 1 sig fig, but I feel like that's too much rounding, so let's just go with 2 sig figs based on 45. So it's gonna be negative 23, roughly, kilojoules of heat are released. So here using q equals mcat we're able to isolate the heat that's involved in the releasing by the water molecule going from 90 degrees Celsius to 45 degrees Celsius.
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Problem
Problem
A sample of copper absorbs 3.53 kJ of heat, which increases the temperature by 25 ºC, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J / g ºC.
A
0.73 kg
B
0.35 kg
C
0.37 kg
D
0.53 kg
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Problem
Problem
Based on their given specific heat capacities which compound would show the greatest temperature change upon absorbing 25.0 J of heat?
A
250.0 g Al
B
250.0 g Cu
C
250.0 g ethanol
D
250.0 g wood
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Problem
Problem
50.00 g of heated metal ore is placed into an insulated beaker containing 822.5 g of water. Once the metal heats up the final temperature of the water is 32.08 ºC. If the metal gains 14.55 kJ of energy, what is the initial temperature of the water?