Respuesta :
We can use the heat equation,
Q = mcΔT
Where Q is the amount of energy transferred (J), m is the mass of the substance (kg), c is the specific heat (J g⁻¹ °C⁻¹) and ΔT is the temperature difference (°C).
Q = 322 J
m = 100.0 g
c = ?
ΔT = (50 - 25) °C = 25 °C
By applying the formula,
322 J = 100.0 g x c x 25 °C
c = 322 J / (100.0 g x 25 °C)
c = 0.1288 J g⁻¹ °C⁻¹
Hence, the specific heat of gold is 0.1288 J g⁻¹ °C⁻¹.
The specific heat of gold is [tex]$\boxed{{\text{0}}{\text{.1288 J}}{{\text{g}}^{-1}}^\circ{{\text{C}}^{-1}}}$[/tex]
Further explanation:
The property is a unique feature of the substance that differentiates it from the other substances. It is classified into two types:
1. Intensive properties:
These are the properties that depend on the nature of the substance. These don't depend on the size of the system. Their values remain unaltered even if the system is further divided into a number of subsystems. Temperature, refractive index, concentration, pressure, and density are some of the examples of intensive properties.
2. Extensive properties:
These are the properties that depend on the amount of the substance. These are additive in nature when a single system is divided into many subsystems. Mass, enthalpy, volume, energy, size, weight, and length are some of the examples of extensive properties.
Specific heat is the amount of heat required to increase the temperature of any substance per unit mass. Its SI unit is Joule (J).
The formula to calculate the heat energy of gold is as follows:
[tex]${\text{Q}}={\text{mc\Delta T}}$[/tex] …… (1)
Here,
Q is the amount of heat transferred.
m is the mass of gold.
c is the specific heat of gold.
[tex]${\text{\Delta T}}$[/tex] is the change in temperature of gold.
Rearrange equation (1) to calculate the specific heat of gold.
[tex]\text{c}=\dfrac{\text{Q}}{\text{m}\Delta\text{T}}[/tex] …… (2)
The temperature change [tex]\left({\Delta {\text{T}}}\right)[/tex] can be calculated as follows:
[tex]${\text{\Delta T}}={{\text{T}}_{\text{f}}}-{{\text{T}}_{\text{i}}}$[/tex] …… (3)
Here,
[tex]${\text{\Delta T}}$[/tex] is the change in temperature.
[tex]{{\text{T}}_{\text{f}}}[/tex] is the final temperature.
[tex]{{\text{T}}_{\text{i}}}[/tex] is the initial temperature.
The value of [tex]{{\text{T}}_{\text{i}}}[/tex] is [tex]25\;^\circ{\text{C}}[/tex] .
The value of [tex]{{\text{T}}_{\text{f}}}[/tex] is [tex]50\;^\circ{\text{C}}[/tex]
Substitute these values in equation (3).
[tex]\begin{aligned}\Delta\text{T}&=50\;^\circ{\text{C}}-25\;^\circ{\text{C}}\\&=25\;^\circ{\text{C}}\end{aligned}[/tex]
The value of m is 100 g.
The value of Q is 322 J.
The value of [tex]${\text{\Delta T}}$[/tex] is [tex]25\;^\circ{\text{C}}[/tex] .
Substitute these values in equation (2).
[tex]\begin{aligned}{\text{Specific heat of gold }}\left( {\text{c}}\right)&=\frac{{{\text{322 J}}}}{{\left( {{\text{100 g}}}\right)\left({25\;^\circ{\text{C}}}\right)}}\\&={\mathbf{0}}{\mathbf{.1288}}\;{\mathbf{J}}{{\mathbf{g}}^{{\mathbf{-1}}}}{\mathbf{^\circ }}{{\mathbf{C}}^{{\mathbf{-1}}}}\\\end{aligned}[/tex]
Learn more:
1. What is the equilibrium constant of pure water at [tex]25\;^\circ{\text{C}}[/tex] ? https://brainly.com/question/3467841
2. Calculate the wavelength of the electron: https://brainly.com/question/6352445
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Thermodynamics
Keywords: intensive, extensive, enthalpy, specific heat of gold, gold, m, Q, initial temperature, final temperature, change in temperature, mass of gold, amount of heat transferred, 0.188 Jg-1oC-1.
