A 237 -g piece of molybdenum, initially at 100.0^∘ C, is dropped into 244 g of water at 10.0^∘ C

A 237 -g piece of molybdenum, initially at 100.0^∘ C, is...

Key Concepts

Specific Heat Capacity

This is a property of a material that indicates the amount of heat required to raise the temperature of one gram (or one kilogram) of the substance by one degree Celsius (or one Kelvin). It is an intrinsic characteristic that helps in comparing how different materials absorb heat energy, and it is crucial in calculations involving thermal processes and energy transfer.

Conservation of Energy

In thermodynamics, the conservation of energy principle states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the context of heat exchange between substances, this principle implies that the total heat lost by the hotter object must equal the total heat gained by the cooler object, assuming no heat is lost to the surroundings.

Heat Transfer Equation

The heat transfer equation, represented as Q = m · c · ?T, relates the quantity of heat exchanged (Q) to the mass (m) of the substance, its specific heat capacity (c), and the change in temperature (?T). This equation is fundamental in solving problems in thermodynamics, especially when calculating the energy required to change the temperature of a substance.

Thermal Equilibrium

Thermal equilibrium refers to the state reached by two or more objects in thermal contact when they no longer transfer heat between them, resulting in a uniform temperature throughout the system. This concept is essential in calorimetry problems, as it allows for the application of the conservation of energy principle to determine the final equilibrium temperature and associated energy exchanges.

Transcript

00:01 Okay, so in this problem, we are asked to find the specific heat capacity of molybdom, of malibdenum, and we are given the starting mass of the molybdenum, the initial temperature, and then we are told that it is dropped into a certain amount of water at a certain temperature, and that the system comes to a final temperature equilibrium at 15 .3 degrees celsius.

00:29 So, we know that the heat, let's fix that really quick, we know that the heat that comes into the water must be equal, or i should say, must be opposite of the heat that leaves the molybdenum.

00:55 So we can relate these using our favorite equation, mc delta t, of the water is equal to mc.

01:07 Delta t of the molybdenum and i'll abbreviate that mb and here we'll label this water all right and so what do we have we have the mass of the maledinum 237 grams we have the the change in temperature because we're told that it starts at 100 and drops to 15 .3 we are looking for our specific heat and of course we have our mass of water we know the specific heat of water is 4 .24, and we also have the change in temperature of the water.

01:45 So let's orient our equation to look to find what we are looking for.

01:52 Mc, actually i'll do this in blue to make this easier.

01:56 So mc delta t of the water, and we can divide over the mass and the change in temperature of our molybdenum, and that will give us the specific heat of molybidum.

02:13 So let's just plug in our numbers here and see what we get so there's 244 grams of water specific heat is 4 .184 joules per gram kelvin and the change in temperature is 15 .3 minus 10 so 5 .3 degrees celsius 5 .3 and then on bottom we have we have 237 grams.

02:57 Fix that writing really quick, 237 grams times our change in temperature.

03:08 Here, let's make sure i include our negative here...

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