Ideal Gas Relations and Graph Analysis

Ideal Gas Laws

• An ideal gas graph shows the relationship between pressure and volume.
• At constant pressure, the volume of a gas is directly proportional to the temperature.

Physics Problems

• A body's ability to resist a change in temperature is determined by its specific heat capacity.
• The volume of a copper cube can be calculated by finding the cube of its side length (V = s³).
• Convection is the term used to describe the transfer of heat by the movement of a fluid.
• The volume of a gas is directly proportional to the temperature at constant pressure.
• A Celsius temperature can be converted to a Kelvin temperature by adding 273.15.
• The three phases of matter are solid, liquid, and gas.
• Iron is in a solid state at room temperature.
• The change in length of a cylindrical bar can be calculated using the formula ΔL = αL₀ΔT.
• The final temperature of two blocks of different materials in contact can be calculated using the formula Q = mcΔT.
• The heat required to increase the temperature of water can be calculated using the formula Q = mcΔT.
• Surface tension of a liquid can be calculated using the formula γ = ρgh.

States of Matter

• The melting point is the temperature at which a substance changes from a solid to a liquid.
• The boiling point is the temperature at which a substance changes from a liquid to a gas.
• Melting is the change of state from solid to liquid due to the absorption of heat.
• Boiling is the change of state from liquid to gas due to the absorption of heat.
• Condensation is the change of state from gas to liquid due to the removal of heat.

Heating Curve

• A heating curve shows the relationship between temperature and time when heat is supplied to a substance at a constant rate.
• The temperature of a substance increases until it reaches its melting point, then remains constant until all the solid is melted.
• The temperature then increases again until it reaches its boiling point, then remains constant until all the liquid is converted to a gas.

Calculating Heat Required to Increase Temperature

• The heat required to increase the temperature of a substance can be calculated using the formula Q = mcΔT.
• The specific heat capacity of a substance is the amount of heat required to raise its temperature by 1°C.

Table of Materials

• The table provides the properties of different materials, including their density, specific heat, melting point, boiling point, heat of fusion, and heat of vaporization.

Example Problem and Assignment

• The heat required to increase the temperature of a substance can be calculated using the formula Q = mcΔT.
• The specific heat capacity of water is 4.18 J/g°C.

2nd Law of Thermodynamics

• The 2nd law of thermodynamics relates to the efficiency of heat engines and refrigerators.
• The equations for efficiency are:
  • T_C = T_H + (T_H - T_C)*ε
  • T_H = (T_H - T_C)*ε + T_C
  • ε = (T_H - T_C)/T_H
  • ε = 1 - T_C/T_H

General Calculations

• The area of an object can be calculated using the formula A = lw.
• The volume of an object can be calculated using the formula V = lwh.
• Thermal expansion can be calculated using the formula ΔL = αL₀ΔT.

Thermal Expansion

• Linear expansion is a change in length due to a change in temperature.
• Area expansion is a change in area due to a change in temperature.
• Volume expansion is a change in volume due to a change in temperature.
• The formulas for thermal expansion are:
  • ΔL = αL₀ΔT
  • A_f = A_i (1 + 2αΔT)
  • ΔV = βV₀ΔT

Volume Expansion of Liquids

• The volume of a liquid will change by a factor of 1 + βΔT, where β is the volume expansivity and ΔT is the temperature change.
• The apparent expansion of a liquid is given by ΔV_a = βΔV, where ΔV is the real expansion of the liquid.
• The real expansion of the container is given by ΔV_c = γΔV.

Density and Change in Temperature

• The density of a substance changes with a change in temperature.
• If the volume decreases, the density increases.
• The formula for density is ρ_f = ρ_i / (1 + βΔT).