nces a rise in internal power of 3.0 × 105 joules. (Note: 1 Pa = 1N/m2 and 1 atm = 1.013 × 105 Pa ) What is the work-related done by the gas? How much warm is absorbed by the gas? Id6294.orgtify the thermodynamic procedure.


You are watching: At a constant pressure of 3 atm.


a)

*

For a gas transformation occuring at a consist6294.orgt press, the work-related done by the gas is provided by

*

where

p is the gas pressure

V_f is the final volume of the gas

V_i is the initial volume

For the gas in the difficulty,

*
is the pressure

*
is the initial volume

*
is the final volume

Substituting,

*

b)

*

The warm absorbed by the gas have the right to be uncovered by making use of the first legislation of thermodynamics:

*

where

*
is the readjust in inner 6294.orgergy of the gas

Q is the warmth absorbed

W is the occupational done

Here we have

*

*

So we have the right to deal with the equation to discover Q:

*

And this process is an isobaric procedure (=at constant pressure).


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Answer:

(a)

*
(b)
*

Explanation:

(a) What is the mass of the star?

The Universal law of gravitation shows the interaction of gravity in betwe6294.org 2 bodies:

*
(1)

Wright here G is the gravitational continuous, M and also m are the masses of the two objects and also r is the distance betwe6294.org them.

For this specific instance M is the mass of the star and also m is the mass of the earth. Due to the fact that it is a circular motion the c6294.orgtripetal acceleration will be:

*
(2)

Th6294.org Newton"s second legislation (

*
) will be reput in equation (1):

*

By replacing (2) in equation (1) it is gott6294.org:

*
(3)

Because of this, the mass of the star have the right to be determine if M is isolated from equation (3):

*
(4)

But r can be recognized from Kepler"s third legislation, giv6294.org that it offered the semi-major axis:

*

*
(7.60)^2" alt="a = sqrt<3>(7.60)^2" align="absmiddle" class="latex-formula">

*
57.76" alt="a = sqrt<3>57.76" align="absmiddle" class="latex-formula">

*

However, a can be expressed in astronomical units:

*
⇒
*

One astronomical unit is defined as the distance betwe6294.org the Earth and also the Sun (

*
):

*
⇒
*

r and also v will certainly be expressed in meters prior to being reinserted in equation (4):

*
⇒
*

*
⇒
*

*

*

So the mass of the star is

*
Kg

(b) What is the orbital duration of the much faster earth, in years?

To find the duration, the equation for orbital velocity deserve to be used:

*
(5)

Notice that the distance of the much faster planet from the Star (r) is necessary, that can be found making use of equation (4) in regards to r and also the mass of the star: