Heat Formula and Ideal Gas Law Formulas

Heat Formula

Heat is the form of energy which is transferred between two substances at different temperatures. The direction of the flow of energy is from the substance of higher temperature to the substance of lower temperature. Heat is usually measured in units of energy i.e. calories or joules. Heat and temperature should not be used interchangeably, but this is incorrect. The temperature will measure the hotness or coldness of a substance. In this article, we will discuss the heat formula with examples. Let us learn the concept!

Heat Formula

What is the concept behind heat?

Heat is the transfer of kinetic energy from one medium to another medium via energy source. This energy transfer can occur in three different ways which are radiation, conduction, and convection. Heat is a form of energy which produces a change in the temperature of any substance.

Also, the temperature is the average kinetic energy per molecule of that substance. Temperature is measured in different scales as Celsius (C), Fahrenheit (F) and Kelvins (K). Therefore, in a simple way temperature is how hot or cold an object is. On the other hand, heat is the energy that flows from a hotter object to a cooler object.

Due to heat thermal expansion may occur. It is a phenomenon that takes place in solids, liquids, and gases. Almost all substances expand with an increase in the temperatures. For example, due to the heating of air in a hot air balloon, the balloon expands and rises. In every case, thermal expansion occurs in response to the increase in temperature and devices may take advantage of this concept.

Heat by conduction takes place when two objects are kept in direct contact. Also, the temperature of one is higher than the other. The temperature tends to equalize and due to which the heat conduction consists of the transfer of kinetic energy from warmer medium to a cooler one.

We denote heat is denoted by Q.

The Heat formula is:

C = QmΔT

Where,

C	specific heat,
m	mass of the body,
Δ	temperature difference.

We generally use Heat formula to find out the heat transfer, mass, specific heat or temperature difference in a given situation. Heat is expressed in units of Joules (J).

Solved Examples

Q.1: Determine the heat needed to raise a 1 kg of iron from 250° C to 600° C?

Solution:

As given in the problem,

Mass, m = 1 Kg,

Specific heat of iron, C = 0.45 Jg−1°C

Also, temperature difference,

ΔT=700°C–250°C

ΔT=450°C

Now applying the heat formula,

c=QmΔT

rearranging the formula

Q=mcΔT

Q=1×0.45×103×450

= 20.25 J

Q. 2: Determine how much heat energy is lost if 50 Kg water is cooled from 600\degreeC to 200\degreeC. Specific heat of water is given as C=4.2×103JKg−1°C.

Solution:

Given values are,

Mass of water, m = 50 Kg,

Specific heat of water, C = 4.2×103JKg−1°

Temperature difference,

ΔT=–40°

Heat energy by formula is,

Q = mcΔT

Q = 50×4.2×103×(−400)

Q= – 840 J

Ideal Gas Law Formula

An ideal gas is a gas composed of randomly moving point particles that interact only through elastic collisions. Ideal gas is a theoretical concept. The ideal gas concept is beneficial because it follows the ideal gas law. Here we discuss Ideal Gas Law Formula and its applications.

Ideal Gas Law Formula

What is an Ideal Gas Law?

The concept of an Ideal gas is an approximation that helps us to predict the behavior of real gases. The term ideal gas refers to a theoretical gas composed of molecules, which follow a few rules they are:

1. Ideal gas molecules do not attract or repel each other.
2. The ideal gas molecules interact by elastic collision.
3. These molecules themselves take up no volume.
4. Ideal gas molecules are moving point particles that have no volume of themselves.

Ideal Gas Law

The Ideal Gas Law created to show the relationship between pressure, volume, number of moles of gas and temperature. It shows the equation of a hypothetical or theoretical ideal gas. Pressure and volume have an inverse relationship with each other but have a direct relationship with Temperature.

The equation for the Ideal Gas Law is:

P × V = n × R × T

P	Pressure (atm)
V	Volume (L)
n	Number of moles (mol)
R	The Ideal Gas Constant (0.08206 L-atm/mol-K)
T	Temperature (Kelvin)

Derivation of Ideal Gas Law

Ideal Gas Law is a combination of three simple gas laws. They are Avogadro’s Law, Boyle’s Law and Charles’s Law.

Now we derive the Ideal Gas Law.

i) Avogadro’s Law: It states that the volume of a gas is directly proportional to the number of moles.
V∝n—————(1)

ii) Boyle’s Law: It states that the pressure of a gas is inversely proportional to its volume.
V∝1P—————(2)

iii) Charles’s Law: It states that the volume of a gas is directly proportional to its Kelvin temperature.
V∝T—————–(3)

For Ideal Gas Law we combine all the 3 equations, we get
V∝n×TP

To covert the proportionality to equality we use universal gas constant R. We get,
V=n×R×TP

Ideal Gas Law is given as
P × V = n ×R ×T

Solved Examples

Q 1. Calculate the volume 5.00 moles of gas will occupy at 30°Celsius and 765 mm Hg. (R= 8.314 J/mol K)

Answer: The number of moles is n = 5.00moles, temperature is T = 30°C and pressure is P = 765 mmHg, R= 8.314 J/mol K

First, we convert Temperature to Kelvin and Pressure to Atmospheres for the ideal gas equation.

T = 30 + 273 = 303 K

P = 765760 = 1.006 atm

Ideal Gas Law Equation =>  P×V=n×R×T

1.006×(V)=3.00×(0.08314)×(303)

V = 75.123 L

The volume of the gas would be 75.123 Litres

Q 2: How many moles of ‘He’ are contained in a 5- litre canister at 100 KPa and 25 ° C. Take R= 8.314 J/mol K

Answer: Using the Ideal gas equation, n = P×VR×T

Therefore, on substituting the values

T = 25 + 273 = 298

we get,

= 100×5/8.314×298=5002477.572 = 0.2018 moles

Hence, 0.2018 moles of ‘He’ are contained in a 5-litre canister at 100 KPa and 25 ° C