How much energy as heat is required to raise the temperature...

How much energy as heat is required to raise the temperature of 50.00 mL. of water from $25.52^{\circ} \mathrm{C}$ to $28.75^{\circ} \mathrm{C}^{2}$ (Density of water at this temperature $=\mathbf{0 . 9 9 7} \mathrm{g} / \mathrm{mL} .$ )

Key Concepts

Density

Density is the mass per unit volume of a substance. It is critical for converting a given volume of a liquid into its corresponding mass, which is necessary when using formulas that involve mass, such as those calculating the energy changes in a substance.

Specific Heat Capacity

Specific heat capacity is the amount of heat energy required to raise the temperature of one unit of mass of a substance by one degree Celsius. This property is essential for determining how much energy is needed to effect a temperature change in a substance.

Temperature Change (?T)

Temperature change refers to the difference between the final and initial temperatures of a substance. It is a key component in thermal energy calculations because the energy required is directly proportional to the magnitude of this change.

Heat Energy Calculation Formula (Q = m × c × ?T)

This formula is used to calculate the heat energy required to change the temperature of a substance. It combines the mass of the substance (which can be obtained using density if volume is given), its specific heat capacity, and the temperature change, making it a fundamental tool in thermodynamics and thermal physics.

Transcript

00:01 Okay, so for this question, they want us to determine how much heat is needed to raise the temperature of the water from 25 .52 degrees celsius to 28 .75.

00:13 And they give us the volume as 50 militers and the density of h2o as 0 .997 grams per millimeter.

00:22 So the first thing that we should do is we should convert the volume of water to grams of water.

00:31 The reason why is because eventually the equation that we're going to need to solve this question is q is equal to c, which is the specific key constant of that substance, times it by mass in grams, and then times it by delta t.

00:46 So we need mass.

00:47 So what we can do is we know the volume and we know the density, so we can use these two values to solve for mass.

00:54 So mass of water or mass of h2o is equal to density divided by the density.

01:03 Volume right because we know density we know density is mass divided by volume so if we were to multiply both sides by volume we get mass is equal to density times volume and that's exactly what we're doing here so mass of htl is equal to density which is 0 .997 grams per milliliter times it by the volume which is 50 milliliters so i'm giving millimeters the volume of milliliters because the density has milliliters right so we get the mass of h2 o as mass is equal to 49 .85 grams right we have grams now so we know this this value we look on in our textbook and we or we can look online and we should see that's a specific heat capacity specific heat capacity of h2 o is equal to 4 .184 jr per gram times kelvin right so we see that this constant has grams jewels and kelvin so let's convert these temperatures into kelvin right we know that let me erase this we know that the conversion between celsius and kelvin is 273 right so we just add 273 to the celsius to get kelvin right so for ti we should get 298 .52 kelvin and for t final we should get 301 .75 kelvin...

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